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THE NORMAL DISTRIBUTION

A  normal  distribu/on  of  data  means  that  most  of  the  points  in  a  set  of  data  are  close  to  the  "average,"  while  rela/vely  few  points  tend  to  one  extreme  or  the  other.    

DIFFERENT NORMAL DISTRIBUTIONS

Most  data  close  to  mean  Data  spread  out  

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STANDARD DEVIATION

Ò The standard deviation ( ) is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data.

When  the  data  are  pre@y  /ghtly  bunched  together  and  the  bell-­‐shaped  curve  is  steep,  the  standard  devia,on  is  small.  

When  the  data  are  spread  apart  and  the  bell  curve  is  more  flat,  that  tells  you  you  have  a  rela/vely  large  standard  devia,on.    

σ

ONE STANDARD DEVIATION

One  standard  devia/on  

Two  standard  devia/ons  

Three  standard  devia/ons  

34% 34%

13.5% 13.5%

2.5% 2.5%

All together = 99%!

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NORMAL CURVE

The mean and median are the SAME. Mean – balance point Median – cuts area under curve in half

MEN’S HEIGHTS

69”  Mean  is  69”  Standard  Devia/on  is  2.8  

71.8”   74.6”   77.4”  66.2”  63.4”  60.6”  

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MEN’S HEIGHTS

69”  

Michael  Jordan  is  78”  tall  

71.8”   74.6”   77.4”  66.2”  63.4”  60.6”  

OUTLIER

Ò A value that is substantially different from other data in the set.

Ò Michael Jordan’s height is an outlier.

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5

WOMEN’S HEIGHTS

63.6”  Mean  is  63.6”  Standard  Devia/on  is  2.5  

66.1”   68.6”   71.1”  61.1”  58.6”  56.1”